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01 May 2013, 19:29
Kudos
Bookmarks
Hi,
An article was posted 2 days back on their blog and I can't seem to open it now. I have the post saved on my Android app "Pocket". Here's the post in its entirety:
Even if you know the basic rules for questions involving powers and roots, it’s still common to feel some intimidation towards harder-looking GMAT questions.
The “ ” symbol is called the “radical” symbol. You may know the square root, but how comfortable are you with cube roots? For instance:
The “3″ in the above is the “index” of the radical; to simplify radicals, use your knowledge of factors:
64 = 2 x 2 x 2 x 2 x 2 x 2
There are six 2’s in 64. Since the index is 3, we know we need three of the same number to pull it out from underneath the radical. Exponents and radicals appear most frequently on the GMAT in data sufficiency questions dealing with number properties:
If z x ?
(1) x2 > 4
(2) x > -2
Because you know your exponent rules, you know that whether x2 > x is true is dependent on what kind of number x is. Let’s quickly plug in:
If x = 1, then x2 > x = 1 > 1. Not true.
If x = ½, then x2 > x = ¼ > ½. Not true.
If x = 0, then x2 > x = 0 > 0. Not true.
If x = -1/2, then x2 > x = ¼ > -1/2. True.
If x = -1, then x2 > x = 1 > -1. True.
We can see that when x is negative, the answer will be YES. When x is positive, the answer will be NO. For Statement (1), x could be negative or positive, so insufficient. For (2), x could still be negative or positive. If we combine, x > 2 in order to satisfy both conditions.
The correct answer is (C).
The rules don’t change because powers and roots are combined with a secondary concept, such as inequalities here, so don’t let a combination of ideas throw you as you practice!
I'm having trouble understanding why the answer is C. For x^2 to be greater than x, x needs to have a 'value' greater than 1. For any x in -1 x.
Please help me understand.
Thank you!
An article was posted 2 days back on their blog and I can't seem to open it now. I have the post saved on my Android app "Pocket". Here's the post in its entirety:
Even if you know the basic rules for questions involving powers and roots, it’s still common to feel some intimidation towards harder-looking GMAT questions.
The “ ” symbol is called the “radical” symbol. You may know the square root, but how comfortable are you with cube roots? For instance:
The “3″ in the above is the “index” of the radical; to simplify radicals, use your knowledge of factors:
64 = 2 x 2 x 2 x 2 x 2 x 2
There are six 2’s in 64. Since the index is 3, we know we need three of the same number to pull it out from underneath the radical. Exponents and radicals appear most frequently on the GMAT in data sufficiency questions dealing with number properties:
If z x ?
(1) x2 > 4
(2) x > -2
Because you know your exponent rules, you know that whether x2 > x is true is dependent on what kind of number x is. Let’s quickly plug in:
If x = 1, then x2 > x = 1 > 1. Not true.
If x = ½, then x2 > x = ¼ > ½. Not true.
If x = 0, then x2 > x = 0 > 0. Not true.
If x = -1/2, then x2 > x = ¼ > -1/2. True.
If x = -1, then x2 > x = 1 > -1. True.
We can see that when x is negative, the answer will be YES. When x is positive, the answer will be NO. For Statement (1), x could be negative or positive, so insufficient. For (2), x could still be negative or positive. If we combine, x > 2 in order to satisfy both conditions.
The correct answer is (C).
The rules don’t change because powers and roots are combined with a secondary concept, such as inequalities here, so don’t let a combination of ideas throw you as you practice!
I'm having trouble understanding why the answer is C. For x^2 to be greater than x, x needs to have a 'value' greater than 1. For any x in -1 x.
Please help me understand.
Thank you!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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02 May 2013, 11:26
Kudos
Bookmarks
I am also stumped with this question.
Is x2 > x ?
(1) x2 > 4
(2) x > -2
is \(x^2\)>x --------> is \(x^2\)-x>0 ---------> is x(x-1)>0
We know product of two positive integers is positive and product of two negative integers is also positive
So either both x and (x-1) are positive. That means x>o and x-1>0 --------> x>o and x>1
or both x and (x-1) are negative. That means x<o and x-1<0 --------> x<o and x<1
Now we we need to consider outermost intervals of both possibilities. That means x>1 and x<0
So our question turn out to be Is x>1 or x<0 ????
S1) \(x^2\) > 4 --------> \(x^2\)-4>0 ---------> (x-2)(x+2)>0
either both are positive x-2>0 and x+2>0 that means x>2 and x>-2
or both are negative x-2<0 and x+2<0 that means x<-2 and x<2
After considering outermost intervals of both possibilities we can conclude that x is greater than 2 or less than -2, which is sufficient to answer the question.
Regards,
Narenn
Is x2 > x ?
(1) x2 > 4
(2) x > -2
is \(x^2\)>x --------> is \(x^2\)-x>0 ---------> is x(x-1)>0
We know product of two positive integers is positive and product of two negative integers is also positive
So either both x and (x-1) are positive. That means x>o and x-1>0 --------> x>o and x>1
or both x and (x-1) are negative. That means x<o and x-1<0 --------> x<o and x<1
Now we we need to consider outermost intervals of both possibilities. That means x>1 and x<0
So our question turn out to be Is x>1 or x<0 ????
S1) \(x^2\) > 4 --------> \(x^2\)-4>0 ---------> (x-2)(x+2)>0
either both are positive x-2>0 and x+2>0 that means x>2 and x>-2
or both are negative x-2<0 and x+2<0 that means x<-2 and x<2
After considering outermost intervals of both possibilities we can conclude that x is greater than 2 or less than -2, which is sufficient to answer the question.
Regards,
Narenn
02 May 2013, 23:38
Kudos
Bookmarks
The explanation to this problem is incorrect.
Is x^2 > x ?
(1) x^2 > 4
(2) x > -2
Statement 1: x^2>4 implies that either x>2 or x<-2, if x =3 then the answer to the question is Yes(9>3). In general, any number greater than 1 when squared is greater than the original number so the answer is Yes for all values of x greater than 2. If we consider the case of x<-2, here the square of x will always be positive and that will always exceed x, again the answer is Yes. Sufficient.
Statement 2: x > -2. If x = -1.5, then the answer is Yes, but if x = 1/2, then the answer is No. One can also use x = 0 or x = 1 to show No. Insufficient.
Answer is A.
Dabral
Is x^2 > x ?
(1) x^2 > 4
(2) x > -2
Statement 1: x^2>4 implies that either x>2 or x<-2, if x =3 then the answer to the question is Yes(9>3). In general, any number greater than 1 when squared is greater than the original number so the answer is Yes for all values of x greater than 2. If we consider the case of x<-2, here the square of x will always be positive and that will always exceed x, again the answer is Yes. Sufficient.
Statement 2: x > -2. If x = -1.5, then the answer is Yes, but if x = 1/2, then the answer is No. One can also use x = 0 or x = 1 to show No. Insufficient.
Answer is A.
Dabral
